It is often required to pre-heat a treatment fluid for use in a well for achieving a higher reaction rate during various operations.
In general, the rate of a chemical reaction increases with increasing temperature. The Arrhenius equation (Equation 1) describes the temperature dependence of reaction kinetics. The Arrhenius equation gives the dependence of the rate constant K of a chemical reaction on the absolute temperature T in Kelvin, where A is a pre-exponential factor, Ea is the activation energy, and R is the universal gas constant:K=Ae−Ea/(RT)  Eq. (1)
For example, the rate of a chemical treatment for removing barium sulfate scale (mass) is a function of temperature and time. At less than about 77° F. (25° C.), the reaction rate is very slow and increasing the contact time only very gradually increases the amount of chemically removed scale. For example, at 68° F. (20° C.) after about 24 hours total contact time, the amount of dissolved barium ion of a scale is only about 8,000 ppm. However, at a higher temperature greater than about 77° F. (25° C.), the reaction rate increases and the amount of dissolved barium ion increase linearly with time after an initial contact period of about 3 hours. At 86° F. (30° C.) after about 24 hours total contact time, the amount of dissolved barium ion of the scale is about 25,000 ppm. At 185° F. (85° C.) after about 24 hours total contact time, the amount of dissolved barium ion of the scale is about 80,000 ppm. In general, for chemical removal of an inorganic scale such as barium sulfate, a higher temperature or longer contact time is required for effectiveness of the job.
Similarly, chelant-based matrix stimulation generally requires a temperature greater than about 250° F. (120° C.) for better results. Well operators are trying to use chelant-based systems instead of conventional acidizing systems because these fluid systems reduce the handling risks usually associated with conventional acids. However, their applicability is generally limited to naturally high temperature wells because of the reaction kinetics.
Conventionally, a treatment fluid can be pre-heated at the well site and pumped downhole for a specific purpose. The purpose of the pre-heating is to provide a higher temperature and reaction rate downhole. Unfortunately, as a pre-heated treatment fluid is pumped down the wellbore, heat energy may be lost to the wellbore surroundings and the fluid may become cooled.
In this situation, a higher pumping rate is required to reduce the heat loss and fluid cooling so that the temperature of the fluid will be higher when it reaches the desired treatment zone. FIG. 1 is an example of fluid heat loss as a function of pumping rate. More particularly, FIG. 1 shows a WELLCAT™ temperature simulation of an estimated temperature profile for 40 m3 volume of an aqueous fluid pre-heated to about 158° F. (70° C.) against true vertical depth (TVD) in meter for an exemplary vertical wellbore in a cold environment having a 24 inch surface casing to 500 meters TVD and a 7 inch producing tubing string to 600 meters TVD as a function of pumping rate in liters/minute (lpm). In the example of FIG. 1, if the pumping rate is less than 2 barrels/minute (bpm) (a barrel of oil contains 159.6 liters), then the fluid cools down significantly by the time it reaches the desired depth. If the pumping rate is greater than about 2 bpm, the fluid still cools down but there is slightly less heat loss compared to a lower pumping rate and a higher temperature at depth is obtained as can be seen from FIG. 1.
Unfortunately, a higher pumping rate presents another problem. In general, the higher the pumping rate, the shorter the contact time for the fluid in a portion of a well. The contact time can be calculated using Equation 2, where tcontact is fluid contact time, Vtreatment is the volume of the treatment fluid, and Q is the pumping rate, such that the time of fluid contact is an inverse function (f) of the pumping rate.
                              t          contact                =                                            V              treatment                        Q                    =                      f            ⁡                          (                              1                Q                            )                                                          Eq        .                                  ⁢                  (          2          )                    
Therefore, if the pumping rate is too high, even if the temperature is sufficient, the contact time may be too short for an effective treatment. In addition, sometimes it is not possible to pump a treatment fluid at a sufficiently high rate to maintain an adequate fluid temperature due to surface or bottomhole pressure limitations.
Also, the costs of pre-heating a treatment fluid are high. On an offshore platform, it may require brining in specialized boats or equipment for such operations. Therefore, there are major limitations to methods requiring a pre-heated treatment fluid that reduce the usefulness of such treatments.